Ravi Shankar may be 91 years old, but the memory of June 1971 remains vivid. "I was in Los Angeles," says India's greatest classical musician, "hearing about this terrible tragedy: 100,000 refugees coming into Kolkata, and yet almost nobody knew about it."

The previous November, the Bhola cyclone had ravaged East Pakistan and West Bengal, killing 500,000 people and displacing thousands more. The disaster and its catastrophic aftermath exacerbated existing tensions between the people of East Pakistan and the Pakistani government, leading to the liberation war of 1971 and, later that year, the creation of the independent state of Bangladesh. "I felt I had to do something," Shankar says. "I was in this terrible state of mind when George [Harrison] came to LA for a few days. He saw I was looking so sad, he was really concerned, and so I asked if he could help me. Immediately he called his friends."

Almost exactly 40 years ago, on Sunday 1 August 1971, Shankar, Harrison and those "friends" – among them Bob Dylan, Eric Clapton, Leon Russell and Ringo Starr – staged rock's first mass act of philanthropy, at Madison Square Garden in New York. Harrison, whom Shankar lovingly describes as "my student, my brother, my son, all combined," was enjoying his peak years as a solo superstar. His presence alone ensured that the concert was more than just a worthy cause, in accordance with what we might call Geldof's First Law of the Charity Gig: "The only responsibility the artist has is to create good art," says the man behind Live Aid. "They only fail when they create bad art."

The Concert for Bangladesh scored high on those terms, despite the fact Harrison was, according to his first wife, Pattie Boyd, "extremely nervous. He had to really steel himself to do it." Of the gig itself, Boyd recalls: "You could feel the electricity in the air. It was a momentous occasion. Afterwards there was a feeling of a huge elation. There was lots of talk, lots to deal with. It was too big to just disappear."

Rather than vanish, it expanded. The Concert for Bangladesh raised $243,000 overnight, and spawned a single (Harrison's typically literal Bangladesh, specially written for the occasion), as well as a triple album and a film. It has since raked in $17m for Unicef, funding projects not only in Bangladesh but in trouble spots from Angola to Romania, and is currently the focus of a Month of Giving in aid of the famine in the Horn of Africa. But not everything it achieved can be so easily measured. In paving the way for popular music to explore what Americans like to call its "better self", it still encapsulates much of what is perceived to be the best and worst about rock fundraising: a pile of money, heightened awareness for a clear cause, and a rich cultural and musical legacy on the plus side; confusion, mismanagement, excess and ego on the other.

Having hosted the concert with entirely honourable intentions, Harrison stumbled into what has become a perennial problem: getting the cash to the intended destination. "I don't know how much money actually reached where it should have gone, early on," Boyd says, recalling that Harrison believed that some of it "went walkabout".

"It was uncharted territory, the scale of it," says Jonathan Clyde, of Apple (the Beatles' company, not the tech company), who oversees the Concert's legacy, alongside Harrison's widow, Olivia. "The money did eventually reach Bangladesh, although perhaps not in time to help the refugees at that point. The big mistake was that Unicef wasn't chosen beforehand, and so the IRS [the US tax service] took the view that because the charity wasn't involved in the mounting of the concert, they'd take their cut. This distressed George hugely, it really angered him. There was an ongoing tussle for years, but I'm afraid even now the IRS still take their slice."

Many of these lessons have been learned by those seeking to replicate Harrison's pioneering work, but raising cash through making music remains oddly inefficient. "It's simply unavoidable that there will be costs which must be recovered," says Brendan Paddy, communications director at the Disaster Emergency Committee (DEC), which received half the £1.3m proceeds from Everybody Hurts, the charity single released last year in response to the Haitian earthquake. "It's a balance between keeping those costs down and making it happen quickly, and the public finds that difficult to understand and accept. If your single concern is that every penny of your donation goes to the cause, then you may well find a more efficient way of giving, but that's not really the point."

So what is the point? For all its problems, the Concert for Bangladesh resonated because it united those two lightning rods for 60s idealism – Dylan and, in the form of Harrison and Starr, the Beatles – at a time when music was still regarded as a counter-cultural force powerful enough to change the world. The result, Clyde says, "put Bangladesh on the map. For the generation involved in the war of liberation it meant a huge amount. It helped their independence become recognised."

The Concert for Bangladesh did more than simply raise money, it left a deep imprint on the times. So did Live Aid, partly because it was the first major music event given blanket TV coverage, but also because Geldof, born in 1951 and very much a child of 1968, the high watermark of pop and politics, understood the relationship between the two and how it could be harnessed. In an age of defined ideological divisions, framed by the 1984/85 miners' strike, Live Aid tapped into a desire among musicians to address social issues, and a willingness among audiences to accept that.

In today's fragmented, post-ideological climate, that wider imperative struggles to survive. Spearheaded by Simon Cowell – arguably the only man with the necessary clout and contacts to organise an emergency charity single in a matter of days – Everybody Hurts featured, among others, Westlife, Leona Lewis, Alexandra Burke and James Blunt, none of whom appear to believe that social usefulness should extend to the content of their songs. "There aren't enough new artists writing and recording music as a reaction against the environment they live in," says Harvey Goldsmith, who promoted Live Aid, Live 8 and executive produced Live Earth. "That's definitely a problem when it comes to these things."

Clarity of purpose is crucial for the success of a charity concert, and if the artists aren't providing it, it becomes even more important for the event itself to make its aims known. Live Earth bombed because it lacked the imprimatur of a figurehead or a clearly defined aim, while the clash between the message (raising climate change awareness) and the method (pop stars jetting in to stage energy-guzzling megagigs) – was horribly discordant. Reviews were poor, TV ratings tanked, and its achievements were negligible. "There were some issues," admits Goldsmith. "I only want to do events where there's a result at the end of it that you can see. With Live Earth, it was purely about awareness. Did it have specific objectives? Well, it wasn't a problem solver."

But is raising awareness enough? Rachel Weingarten, a US promoter and marketing strategist who has helped a number of musicians – including Wyclef Jean and Christina Aguilera – engage with charitable causes, says: "That catchword 'awareness' can definitely be abused. It's often a way of softening the blow, of saying, 'Well, we didn't raise any money, but …' That can be a slippery slope."

Regardless of the success of a charity concert, accusations of hypocrisy and self-promotion are sure to follow. Such criticisms aren't new. Even in 1971, Boyd says, "we all got limos back to the hotel", while Shankar recalls that "in the beginning everyone involved was quite ignorant" of the cause. Live Aid saved countless lives (the Band Aid Trust has donated over £80m to famine-relief projects) but there was no shortage of dissent. Morrissey called it "the most self-righteous platform ever in the history of popular music". Chumbawamba, meanwhile, titled their 1986 debut album Pictures of Starving Children Sell Records. "We've always had a power relationship with poorer countries, whether military or cultural, and Live Aid enhanced that," says Chumbawamba's Boff. "'We are the helpers, and you are the helpless.' There was no questioning of what charity actually does. Why is this situation happening? Is it anything to do with us in the first place? And it was such an ostentatious display: all the bickering backstage, all the cocaine …"

Just how cynical should we be? The producer of Everybody Hurts, Steve Robson, describes that recording session as "very moving. Everyone talked about Haiti and how they wanted to help. I don't think for a minute that there were any other motivations." Billy Bragg, whom one might expect to be suspicious of rock star noblesse oblige, agrees: "When pop stars recognise that there's a world beyond the end of their leotard, we should give them the benefit of the doubt. If you start attacking that, you end up looking at the village fete and thinking: 'What's the point?'"

Weingarten is more equivocal. She argues that, for some, choosing a charity is not so different from launching a new perfume or brand endorsement. "Big ideas like Band Aid were mostly heart and very little ego, and they achieved a lot," she says. "Now it's become partially a business opportunity. I get calls all the time: 'Listen, this person needs to clean up their image, what can we do?' It's win-win, but the general public doesn't like to hear that people do these things to whitewash their reputation."

Arguably, mixed motives ultimately don't matter much. Bob Geldof, for one, warns against expecting miracles from musicians. "Charity gigs raise cash and awareness," he says. "That's good and crucial, but they deal with the symptoms of a greater malaise whose structures are usually and ultimately political and economic. That requires a longer, more tedious road to travel to affect actual change. That can suit some musicians, if that's what interests them, but it usually doesn't, no more than it would interest anyone else. That's OK. Those performing have already done more than enough by contributing their abilities."

Despite concerns that it doesn't encourage sustained giving, or that it fails to acknowledge underlying issues, the awkward dance between music and charity will continue, largely because the ultimate argument remains as compelling as it did 40 years ago. Few other fundraising methods combine the ability to raise lots of money and public awareness almost overnight.

"I've been to Bangladesh and I can't tell you the love and respect they have for what we did," Shankar says. "It was like a miracle." Four decades later, the DEC saw "a huge spike" in direct donations following the Helping Haiti single. "People had issues with the song, with Cowell, with using the most populist end of the music industry," says Brendan Paddy. "But they either supported the single anyway, or thought: 'Bugger the song, I'll just donate a tenner.' Often that was people we wouldn't usually reach, on Facebook, Twitter or in music magazines."

Yet the suspicion lingers that music and charity haven't always brought out the best in one another. A recurring theme is that Live Aid and its ilk helped create a cosily consensual environment that ultimately tamed rock'n'roll's historically oppositional streak. This has had an increasingly adverse effect on music's willingness to engage with issues. In an age when overdubbing two lines on a fundraising single or tweeting for a worthy cause has largely replaced direct social comment in songs, perhaps the really pressing question isn't whether music has been good for charity, but whether charity been good for music.